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I usually toss out my breeding leftovers (marked) when I'm done; though this means people get some varied things (some people are getting 2 IV ones others are getting 4 or 5), I only toss out the ones with the right nature/ability onto WT so at least people can use it for breeding.
I get something like 90% junk, but I've gotten about 4-5 breeding parents from it, including a Japanese Fletchling with 4 IVs and Adamant/Gale Wings. I pretty quickly got a 5 IV one (wrong IVs, but still) to mix with it, then in a horrible string of luck managed to breed three and a half more boxes of Gale Wings and probably two boxes of Big Pecks (not sure because I usually just released them from my sorting box) before I finally lucked out and got a 6 IV one. Ended up sending two of those boxes out and got a couple of decent breeders, including a Klefki that I think is going to be my next project.
I've noticed that, when I'm getting trades from JP people, I either get first route trash or 4 IV+ breeding stock. Doesn't seem to be an in-between like with other nationalities.